Efficient and robust 3D reconstruction: Absolute phase extraction algorithm based on three gray images.

• Innovative efficiency: Introducing a novel absolute phase extraction algorithm requiring only three grayscale images for high-speed 3D reconstruction. • Robust performance: Demonstrating resilience to environmental factors such as noise, reflectivity variations, and shadows commonly encountered in practical measurement scenarios. • Adaptive error correction: Proposing an error correction technique that adaptively self-corrects non-linear errors in the phase obtained through the algorithm, ensuring enhanced accuracy. • Cost-effective solution: Eliminating the need for additional pattern-assisted phase unwrapping or expensive equipment, providing a cost-effective 3D measurement solution. • Dynamic scene advantage: Outperforming in dynamic scenes, achieving high-quality reconstruction with minimal projected fringes and reduced computational requirements. The structured light three-dimensional (3D) measurement technology based on optical metrics has gained increasing applications, and there is a growing demand for capturing transient trajectory changes in dynamic scenes. Conventional temporal phase unwrapping (TPU) approaches often require multi-frequency fringe patterns for application. However, the inevitable conflict arises between the number of projected fringe patterns and the measurement speed. This paper proposes a highly accurate and robust 3D measurement method using only 3-step phase-shifting fringe patterns. To precisely reconstruct the 3D shape using the fewest fringe patterns, it is essential to extract as much information as possible from the available patterns. Therefore, we calculate the wrapped phase distribution using 3-step phase-shifting fringe patterns to ensure accuracy. Simultaneously, the trapezoidal phase-shifting method is employed to calculate the intensity ratio distribution. Through the proposed region-based indexing method, the intensity ratio map is transformed into an unwrapped phase map. Additionally, a novel self-correction method is introduced to correct the non-linear errors in the unwrapped phase map, which is then utilized for the calculation of the fringe order required for phase unwrapping. This high-speed measurement method utilizes only 3-step phase-shifting fringe patterns while retaining the advantages of TPU, meeting the requirements of high-speed and full-field measurements. Experimental results on both static and dynamic scenes validate the effectiveness and versatility of the proposed method, demonstrating its flexibility and simplicity in application. In our 3D measurement system, the method achieves 3D reconstruction of the dynamic object's trajectory at a measurement speed of 107 frames per second. [ABSTRACT FROM AUTHOR]